Possible dual effect of synapses that are putatively purely excitatory or purely inhibitory: bases in stability theory and implications for neural network behavior

Depolarization of an excitable membrane has a dual effect; excitatory in that it causes rapid opening of calcium and/or sodium channels but inhibitory in that it also causes those channels to inactivate. We considered whether apparently paradoxical or dual behavior might be exhibited by excitatory and inhibitory synaptic inputs. We used the classic Hodgkin-Huxley model for voltage-gated channels plus leakage channels of appropriate selectivity for ligand-gated postsynaptic channels. We summarize a model cell's behavior by calculating elicited firing frequency as a function of reversal potential and conductance of summed synaptic inputs, using stability theory and direct simulations. Dual behavior is elicited in the model with reasonable densities of ligand-gated channels. Thus a particular synaptic input to a neuron may be either excitatory or inhibitory depending on simultaneous activity of other synaptic inputs to the cell. This input-output map may give rise to biologically realistic and rich behaviors as an element of computed neural networks, and still be computationally tractable.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

Towards a general theory of neural computation based on prediction by single neurons

Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise"). A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of undifferentiated neurons, each implementing similar learning algorithms.     

A Neuron Model with Spatially Distributed Synaptic Input

I have assembled a neuron model simulating contiguous patches of nerve cell membrane. With this model I have examined the functional significance of different spatial and temporal distributions of synaptic inputs. The model consists of two terminal electronic analogue circuits with inputs controlled by a LINC computer. One terminal represents the inside of a membrane patch, the other represents the outside. Two circuit designs are used: one simulates spike-generating regions of the neuron, the other simulates subthreshold activity in inexcitable regions. To simulate a neuron, patches are assembled in various spatial arrangements by suitable connection to the “intracellular” nodes. Thus the relation of neuron geometry to aspects of spatiotemporal summation of synaptic inputs can be investigated readily. Performance of the model is assessed by comparison with results from microelectrode studies in the cochlear nucleus of the cat. In particular, the peristimulus time (PST) histogram and averaged membrane potential are used for quantitative comparison. The model suggests that the geometry of the neuron's receptive surface can account for a wide variety of physiologically observed behavior, particularly in response to dynamic stimuli.     

Complex dynamics of a neuron model with discontinuous magnetic induction and exposed to external radiation

The last two decades have seen many literatures on the mathematical and computational analysis of neuronal activities resulting in many mathematical models to describe neuron. Many of those models have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Only recently researchers have proposed a new neuron model based on the electromagnetic induction theorem, which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. While the flux coupling of the membrane is considered equivalent to a memductance function of a memristor, standard memductance model of \(\alpha + 3\beta \phi^{2}\) has been used in the literatures, but in this paper we propose a new memductance function based on discontinuous flux coupling. Various dynamical properties of the neuron model with discontinuous flux coupling are studied and interestingly the proposed model shows hyperchaotic behavior which was not identified in the literatures. Furthermore, we consider a ring network of the proposed model and investigate whether the chimera state can emerge. The chimera state relates to the state with simultaneously coherence and incoherence in oscillatory networks and has received much attention in recent years.     

Dynamics of action potential initiation in the GABAergic thalamic reticular nucleus in vivo

Understanding the neural mechanisms of action potential generation is critical to establish the way neural circuits generate and coordinate activity. Accordingly, we investigated the dynamics of action potential initiation in the GABAergic thalamic reticular nucleus (TRN) using in vivo intracellular recordings in cats in order to preserve anatomically-intact axo-dendritic distributions and naturally-occurring spatiotemporal patterns of synaptic activity in this structure that regulates the thalamic relay to neocortex. We found a wide operational range of voltage thresholds for action potentials, mostly due to intrinsic voltage-gated conductances and not synaptic activity driven by network oscillations. Varying levels of synchronous synaptic inputs produced fast rates of membrane potential depolarization preceding the action potential onset that were associated with lower thresholds and increased excitability, consistent with TRN neurons performing as coincidence detectors. On the other hand the presence of action potentials preceding any given spike was associated with more depolarized thresholds. The phase-plane trajectory of the action potential showed somato-dendritic propagation, but no obvious axon initial segment component, prominent in other neuronal classes and allegedly responsible for the high onset speed. Overall, our results suggest that TRN neurons could flexibly integrate synaptic inputs to discharge action potentials over wide voltage ranges, and perform as coincidence detectors and temporal integrators, supported by a dynamic action potential threshold.     

神经元放电阈值的可变性及其意义

神经元能够将不同时空模式的突触输入转化为时序精确的动作电位输出，这种灵活、可靠的信息编码方式是神经集群在动态环境或特定任务下产生所需活动模式的重要基础。动作电位的产生遵循全或无规律，只有当细胞膜电压达到放电阈值时，神经元才产生动作电位。放电阈值在细胞内和细胞间具有高度可变性，具体动态依赖于刺激输入和放电历史。特别是，放电阈值对动作电位起始前的膜电压变化十分敏感，这种状态依赖性产生的生物物理根源包括Na⁺失活和K⁺激活。在绝大多数神经元中，动作电位的触发位置是轴突起始端，这个位置处的阈值可变性是决定神经元对时空输入转化规律的关键因素。但是，电生理实验中动作电位的记录位置却通常是胞体或近端树突，此处的阈值可变性高于轴突起始端，而其产生的重要根源是轴突动作电位的反向传播。基于胞体测量的相关研究显示，放电阈值动态能够增强神经元的时间编码、特征选择、增益调控和同时侦测能力。本文首先介绍放电阈值的概念及量化方法，然后详细梳理近年来国内外关于放电阈值可变性及产生根源的研究进展，在此基础上归纳总结放电阈值可变性对神经元编码的重要性，最后对未来放电阈值的研究方向进行展望。     

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Balancing homeostasis and learning in neural circuits

Neural circuits are remarkably adaptable, providing animals with the ability to modify their behavior on the basis of experience. At the same time, they are extremely robust and maintain stability despite the changes associated with adaptation. This combination of adaptability and stability is difficult to achieve, and it provides a strong constraint on any models of plasticity in neural circuits. New evidence suggests that the effect of action potential timing on synaptic plasticity may be an important element in reconciling homeostasis with adaptability. In particular, spike-timing dependent plasticity can act as both an adaptive and a homeostatic mechanism, controlling overall firing rates and distributions of synaptic efficacies while making neurons selective for certain aspects of their inputs. It can also cause networks that initially represent the present state of a stimulus to predict its future state on the basis of experience, a theoretical result supported by experimental data in behaving rats.     

The effects of neomycin on membrane properties and discharge activity of an isolated sensory neuron

The effects of neomycin sulfate were examined upon the discharge activity and electrical membrane properties of an isolated invertebrate sensory neuron, the crayfish stretch receptor neuron. Neomycin depressed cell discharge activity in a concentration-dependent manner over the concentration range of 0.01-1.0 mM. Significant concentration-related increases were observed in the resting membrane potential and the width of the orthodromic action potential. There was a significant concentration-dependent decrease in the fast rising phase of the antidromic action potential. Significant changes also were observed in other electrical properties such as membrane resistance, but these were found not to be concentration related. The most significant change was membrane hyperpolarization, which could account for the depression of cell discharge activity. The observed changes are consistent with a neomycin-induced change in the membrane potassium conductance. It is proposed that the neural effect of neomycin is a selective interaction with the neuronal membrane phospholipids.     

Synaptic modification in neural circuits: a timely action

Long-term modification of synaptic strength is thought to be the basic mechanism underlying the activity-dependent refinement of neural circuits and the formation of memories engrammed on them. Studies ranging from cell culture preparations to humans subjects indicate that the decision of whether a synapse will undergo strengthening or weakening critically depends on the temporal order of presynaptic and postsynaptic activity. At many synapses, potentiation will be induced only when the presynaptic neuron fires an action potential within milliseconds before the postsynaptic neuron fires, whereas weakening will occur when it is the postsynaptic neuron that fires first. Such processes might be important for the remodeling of neural circuits by activity during development and for network functions such as sequence learning and prediction. Ultimately, this synaptic property might also be fundamental for the cognitive process by which we structure our experience through cause and effect relations.     

Brain oscillations,medium spiny neurons,and dopamine

1. The striatum is part of a multisynaptic loop involved in translating higher order cognitive activity into action. The main striatal computational unit is the medium spiny neuron, which integrates inputs arriving from widely distributed cortical neurons and provides the sole striatal output.2. The membrane potential of medium spiny neurons' displays shifts between a very negative resting state (down state) and depolarizing plateaus (up states) which are driven by the excitatory cortical inputs.3. Because striatal spiny neurons fire action potentials only during the up state, these plateau depolarizations are perceived as enabling events that allow information processing through cerebral cortex – basal ganglia circuits. In vivo intracellular recording techniques allow to investigate simultaneously the subthreshold behavior of the medium spiny neuron membrane potential (which is a reading of distributed patterns of cortical activity) and medium spiny neuron firing (which is an index of striatal output).4. Recent studies combining intracellular recordings of striatal neurons with field potential recordings of the cerebral cortex illustrate how the analysis of the input–output transformations performed by medium spiny neurons may help to unveil some aspects of information processing in cerebral cortex – basal ganglia circuits, and to understand the origin of the clinical manifestations of Parkinson's disease and other neurologic and neuropsychiatric disorders that result from alterations in dopamine-dependent information processing in the cerebral cortex – basal ganglia circuits.     

Stability of the memory of eye position in a recurrent network of conductance-based model neurons

Studies of the neural correlates of short-term memory in a wide variety of brain areas have found that transient inputs can cause persistent changes in rates of action potential firing, through a mechanism that remains unknown. In a premotor area that is responsible for holding the eyes still during fixation, persistent neural firing encodes the angular position of the eyes in a characteristic manner: below a threshold position the neuron is silent, and above it the firing rate is linearly related to position. Both the threshold and linear slope vary from neuron to neuron. We have reproduced this behavior in a biophysically plausible network model. Persistence depends on precise tuning of the strength of synaptic feedback, and a relatively long synaptic time constant improves the robustness to mistuning.     

Nitric oxide is an activity-dependent regulator of target neuron intrinsic excitability

Activity-dependent changes in synaptic strength are well established as mediating long-term plasticity underlying learning and memory, but modulation of?target neuron excitability could complement changes in synaptic strength and regulate network activity. It is thought that homeostatic mechanisms match intrinsic excitability to the incoming synaptic drive, but evidence for involvement of voltage-gated conductances is sparse. Here, we show that glutamatergic synaptic activity modulates target neuron excitability and switches the basis of action potential repolarization from Kv3 to Kv2 potassium channel dominance, thereby adjusting neuronal signaling between low and high activity states, respectively. This nitric oxide-mediated signaling dramatically increases Kv2 currents in both the auditory brain stem and hippocampus (>3-fold) transforming synaptic integration and information transmission but with only modest changes in action potential waveform. We conclude that nitric oxide is a homeostatic regulator, tuning neuronal excitability to the recent history of excitatory synaptic inputs over intervals of minutes to hours.     

Balanced synaptic input shapes the correlation between neural spike trains

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.     

Cellular properties and modulation of the stomatogastric ganglion neurons of a stomatopod,Squilla oratoria

Cellular properties and modulation of the identified neurons of the posterior cardiac plate-pyloric system in the stomatogastric ganglion of a stomatopod, Squilla oratoria, were studied electrophysiologically. Each class of neurons involved in the cyclic bursting activity was able to trigger an endogenous, slow depolarizing potential (termed a driver potential) which sustained bursting. Endogenous oscillatory properties were demonstrated by the phase reset behavior in response to brief stimuli during ongoing rhythm. The driver potential was produced by membrane voltage-dependent activation and terminated by an active repolarization. Striking enhancement of bursting properties of all the cell types was induced by synaptic activation via extrinsic nerves, seen as increases in amplitude or duration of driver potentials, spiking rate during a burst, and bursting rate. The motor pattern produced under the influence of extrinsic modulatory inputs continued for a long time, relative to that in the absence of activation of modulatory inputs. Voltage-dependent conductance mechanisms underlying postinhibitory rebound and driver potential responses were modified by inputs. It is concluded that endogenous cellular properties, as well as synaptic circuitry and extrinsic inputs, contribute to generation of the rhythmic motor pattern, and that a motor system and its component neurons have been highly conserved during evolution between stomatopods and decapods.Abbreviations AB anterior burster neuron - CoG commissural ganglion - CPG central pattern generator - lvn lateral ventricular nerve - OG oesophageal ganglion - pcp posterior cardiac plate - PCP pcp constrictor neuron - PD pyloric dilator neuron - PY pyloric constrictor neuron - son superior oesophageal nerve - STG stomatogastric ganglion - stn stomatogastric nerve     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.     

Excitability of jcBNST Neurons Is Reduced in Alcohol-Dependent Animals during Protracted Alcohol Withdrawal

Alcohol dependence and withdrawal has been shown to cause neuroadaptive changes at multiple levels of the nervous system. At the neuron level, adaptations of synaptic connections have been extensively studied in a number of brain areas and accumulating evidence also shows the importance of alcohol dependence-related changes in the intrinsic cellular properties of neurons. At the same time, it is still largely unknown how such neural adaptations impact the firing and integrative properties of neurons. To address these problems, here, we analyze physiological properties of neurons in the bed nucleus of stria terminalis (jcBNST) in animals with a history of alcohol dependence. As a comprehensive approach, first we measure passive and active membrane properties of neurons using conventional current clamp protocols and then analyze their firing responses under the action of simulated synaptic bombardment via dynamic clamp. We find that most physiological properties as measured by DC current injection are barely affected during protracted withdrawal. However, neuronal excitability as measured from firing responses under simulated synaptic inputs with the dynamic clamp is markedly reduced in all 3 types of jcBNST neurons. These results support the importance of studying the effects of alcohol and drugs of abuse on the firing properties of neurons with dynamic clamp protocols designed to bring the neurons into a high conductance state. Since the jcBNST integrates excitatory inputs from the basolateral amygdala (BLA) and cortical inputs from the infralimbic and the insular cortices and in turn is believed to contribute to the inhibitory input to the central nucleus of the amygdala (CeA) the reduced excitability of the jcBNST during protracted withdrawal in alcohol-dependent animals will likely affect ability of the jcBNST to shape the activity and output of the CeA.